1 The Processes of Computer Graphics -- Object Model Building -- Depiction of Models -- Conclusion -- 2 Numbers, Counting and Measuring -- Natural Numbers -- Integers -- Rational Numbers -- Real Numbers -- Complex Numbers -- Representations of Number -- The Computer Representation of Number -- Boolean Algebra -- Summary -- 3 Coordinates and Dimension: Representations of Space and Colour -- Cartesian Coordinates -- Defining Space by Equations and Inequalities -- Angles -- Trigonometry and Polar Coordinates -- Dimension -- Coordinate Systems in Three Dimensions -- Colour and its Representation -- Summary -- 4 Functions and Transformations: Ways of Manipulating Space -- Functions as Mappings -- Graphs of Functions -- Transformations in 2D -- Transformations in 3D -- Combining Affine Transformations -- Inversion of Affine Transformations -- Inversion of Functions -- Shape Transformation by Function Change -- Conclusions -- 5 Form from Function: Analysis of Shapes -- The Straight Line -- Drawing General Function Graphs -- Graphs of Polynomials -- Calculus: Differentiation -- Calculus: Integration -- Series Expansions -- Calculus and Animation -- The Exponential Function -- The Conic Sections -- Some Standard 3D Forms and their Equations -- Summary -- 6 Matrices: Tools for Manipulating Space -- Matrices in Computer Graphics -- Definition and Notation -- Forms of Matrices -- Operations on Matrices: Addition -- Operations on Matrices: Multiplication -- The Identity Matrix -- Matrices and Equations -- The Inverse of a Square Matrix -- Matrices, Transformations and Homogeneous Coordinates: Two Dimensions -- Matrices, Transformations and Homogeneous Coordinates: Three Dimensions -- Inverse of a Transformation Matrix -- Perspective Projection -- Computer Implementation of Matrix Methods -- Summary -- 7 Vectors: Descriptions of Spatial Relationships -- Definition of a Vector -- Notation -- Addition of Vectors: The Parallelogram and Triangle Laws -- Multiplication of a Vector by a Scalar -- Examples of Vector Quantities -- Vectors in 2D Cartesian Spaces -- Vectors in 3D Cartesian Spaces -- Multiplication of Vectors: The Scalar or Dot Product -- Multiplication of Vectors: The Vector or Cross Product -- Representation of Lines Using Vectors -- Classification of Points against Planes Using Vectors -- Representation of Planes in Standard Form -- Intersection of a Line with a Plane -- Inclusion of a Point in a Triangle -- Reflected and Refracted Rays -- Distance between Two Skew Lines -- Intersection of Two Planes -- Summary -- 8 Geometric Modelling and Fractals: Building Descriptions of Objects -- Data Structures -- Geometric Modelling Systems -- Voxel Modelling Methods -- Constructive Solid Geometry (CSG) -- Boundary Representation (B-Rep) -- Isosurface Modelling -- Fractals -- Fractal Dimension -- Fractals Based in the Complex Plane: Julia and Mandelbrot Sets -- Fractals in Simulation of Natural Phenomena -- Summary -- 9 Splines: Generation of Curves and Surfaces -- Reasons for Splines -- Interpolation -- Bézier Splines for Curve Drawing -- Animation Control Using Cubic Bézier Curves -- Drawing Bézier Curves -- Interpolating Splines for Curve Generation -- Animation Control Using Interpolating Splines -- B-Splines -- Non-Uniform Rational B-Splines: NURBS -- Circles and Other Conic Sections -- Surface Construction Using Bézier Patches -- Surface Generation Based on Other Forms of Curve -- Depiction of Surface Patches -- Summary -- 10 Drawing and Rendering: How to Create Pictures -- What is a 3D Drawing? -- Methods for Rendering -- Hidden Surface Removal -- Flat or Lambert Shading -- Scan Line Methods -- Gouraud Shading -- Phong Shading -- Exact Object Rendering -- Shadows -- Specular Highlights -- Textures -- Ray Tracing -- Radiosity -- Anti-Aliasing -- Summary -- Suggestions for Further Reading -- Mathematical and Scientific Minds -- Understanding of Mathematics -- Computer Graphics in General -- Geometric Modelling -- Fractals and Related Issues -- Journals -- Names.